Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the secondand third-order Lax operators, respectively. From the viewpoint of algebro-geometrical study, this difference lies in hyper-elliptic and non-hyper-elliptic curves. The non-hyper-elliptic curves lead to great difficulty in the construction of alg...

We give a local criterion in terms of a residue current for strong holomorphicity of a meromorphic function on an arbitrary puredimensional analytic variety. This generalizes a result by A Tsikh for the case of a reduced complete intersection.

Let a(z) be a meromorphic function having in the disk |z| < R precisely λ poles. In this work for the (λ−1)th row of the Padé table of a(z) the set of uniform convergence is explicitly obtained. The present note is a supplement to the previous work of the author (J. Approx. Theory, 123(2003), 160-207). In the theory of uniform convergence of the Padé approximants the principal question is if th...

In this paper, we study a uniqueness question of meromorphic functions whose nonlinear differential polynomials share a nonzero small function. The results in this paper improve and extend many known results. 2010 Mathematics Subject Classification: 30D35, 30D30

In this paper, we study the uniqueness problem of nonlinear differential polynomials of meromorphic functions that share one small function a(z). Our results extend the corresponding result obtained by S.S. Bhoosnurmath and Smita R. Kabbur [16]. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

In this paper we generalize the concept of Koliha-Drazin invertible operators by introducing generalized Drazin-1-meromorphic operators. A bounded linear operator T on a Banach space X is said to be 1-meromorphic if every non-zero point its spectrum an isolated point. For say that it there exists S acting such TS = ST, STS S, TST ? 1-meromorphic, while admits Kato-1-meromorphic decomposition pa...

In the paper we consider the problem of uniqueness of meromorphic functions sharing one finite nonzero value or one finite nonzero function with their derivatives and answer some open questions posed by K.W. Yu.

The Borel lemma says that any positive non-decreasing continuous function T satisfies T (r+1/T (r)) ≤ 2T (r) outside of a possible exceptional set of finite linear measure. This lemma plays an important role in the theory of entire and meromorphic functions, where the increasing function T is either the logarithm of the maximum modulus function, or the Nevanlinna characteristic. As a result, ex...